Tensorial Constraints for Commuting Endomorphisms of the Generalized Tangent Bundle

TL;DR

This paper explores tensorial constraints on commuting endomorphisms of the generalized tangent bundle, extending generalized Kähler structures and analyzing their algebraic properties with Gr"obner basis methods.

Contribution

It introduces new tensorial constraints for commuting endomorphisms, generalizing the concept of generalized Kähler structures beyond almost complex cases.

Findings

Identified tensorial constraints extending generalized Kähler structures.

Constructed explicit generators of tensorial ideals.

Applied Gr"obner basis techniques to study these tensors.

Abstract

In this paper we consider families of mutually commuting endomorphisms of the generalized tangent bundle. We identify natural tensorial constraints extending the notion of a generalized K\"ahler structure to endomorphisms that are not necessarily generalized almost complex structures. These tensors form ideals whose generators we explicitly construct and study using Gr\"obner basis techniques.